1. Field of the Invention
This invention relates to a temperature compensating circuit, and more particularly to a circuit of this kind suitable in use for a flow sensor which is adapted to e.g. measure a temperature difference between two points on a chip and detect a flow quantity from the result of such measurement.
2. Description of the Prior Art
FIG. 1 is a perspective view of a flow sensor of a type known as a microbridge flow sensor. The flow sensor as illustrated comprises a pair of temperature sensing elements or resistive elements R.sub.X, R.sub.Y, a heater element H and a base 10 supporting sensor elements R.sub.X, R.sub.Y and heater element H. Base 10 is provided with a depression 20 formed on the upper surface thereof, as shown in FIG. 1, such that the elements R.sub.X, R.sub.Y, H are bridged thereacross. An arrow in the drawing indicates the direction of a flow.
The heater element is heated to a relatively low temperature, e.g., at 60.degree. C. Also, sensor elements are thermally isolated from heater element so that a temperature at element RX on the upstream side of heater element is substantially equal to an ambient temperature T.sub.A .degree.C.
FIGS. 2-4 respectively show a conventional temperature compensating circuit including temperature sensor elements such as resistive elements R.sub.X, R.sub.Y shown in FIG. 1. In FIG. 2, resistive elements R.sub.X, R.sub.Y are serially coupled to constant current sources 1, 2, respectively, at points P1, P2, to form a bridge circuit. Differential amplifier 3 has its input terminals coupled to connecting points P1, P2 to receive a voltage signal Vz (=I(RX-RY)), where I represents a current flowing through the bridge circuit.
FIG. 3 shows a more simplified equivalent circuit which employs resistive elements R1, R2 in place of constant current sources 1, 2. If R.sub.1, R.sub.2 &gt;&gt;R.sub.X, R.sub.Y is satisfied, current I shows a substantially constant value, so that the circuit of FIG. 3 operates similarly to that of FIG. 2.
FIG. 4 is another simplified circuit in which resistive elements R.sub.X, R.sub.Y are connected in series and output Vz is extracted from connecting point P3 between them. Thus, output Vz is expressed by Vz=V(R.sub.X /(R.sub.X +R.sub.Y)). Resistive element R.sub.X, R.sub.Y are assumed to have a resistance-temperature characteristic as shown in FIG. 5. If a resistance value at 0.degree. C. is R.sub.X0, a resistance value R.sub.X at a temperature T is expressed by R.sub.X =R.sub.X0 (1+.alpha.T). Also, a resistance value R.sub.Y at a temperature T is expressed, in the same manner, by R.sub.Y =R.sub.Y0 (1+.alpha.T).
As described above, a temperature at resistive element R.sub.X at the upstream side is substantially equal to an ambient temperature T.sub.A .degree.C. because of a highly insulating material employed to insulate resistive element R.sub.X from the heater element. Therefore, if a difference in temperature values sensed by resistive elements R.sub.X, R.sub.Y is .DELTA.T.sub.D, a temperature of resistive element RY at the downstream side of heater element H is expressed by T.sub.A +.DELTA.T.sub.D .degree.C.
Under the condition as described above, output Vz supplied from the bridge circuit of FIG. 1 to differential amplifier 3 is expressed as follows: ##EQU1##
If .DELTA.T.sub.D is assumed to be zero, in order to see a zero point fluctuation characteristic of output Vz, expression (1) is transformed to the following expression (2): EQU Vz=I{R.sub.X0 -R.sub.Y0 +.alpha.(R.sub.X0 -R.sub.Y0)T.sub.A }(2)
Further assuming that R.sub.X0 is equal to R.sub.Y0, Vz is zero. However, when R.sub.X0 is not equal to R.sub.Y0, e.g., due to variations in a manufacturing process, output Vz is determined by expression (2) and accordingly dependent on an ambient temperature T.sub.A.
In FIG. 3, if R.sub.1, R.sub.2 &gt;&gt;R.sub.X, R.sub.Y stands, the same relationship as the circuit as shown in FIG. 2 is established.
In the circuit shown in FIG. 4, output Vz is expressed by the following expression: ##EQU2##
If .DELTA.T.sub.D is zero, that is, if there is no flow, expression (3) is transformed to the following expression (4): ##EQU3##
It can be seen from expression (4) that even if R.sub.X0 is not equal to R.sub.Y0, due to variations in production, voltage signal Vz is not influenced by ambient temperature T.sub.A since voltage Vz is calculated only by a ratio of resistance values R.sub.X0, R.sub.Y0. However, it is generally difficult to make R.sub.X0, R.sub.Y0 equal to each other, the circuit arrangement of FIG. 4 is more practical than that of FIG. 2.
Thus, in FIG. 4, voltage signal Vz at a reference point where temperature difference .DELTA.T.sub.D between sensor elements R.sub.X, R.sub.Y is zero is expressed as (3) minus (4): ##EQU4##
If change in .DELTA.T.sub.D is small and if 1+.alpha.T.sub.A &gt;&gt;.alpha..DELTA.T.sub.D stands, Vz' is expressed by the following approximation (6): ##EQU5##
As is apparent from approximation (6), voltage signal Vz is influenced by ambient temperature T.sub.A such that, when .alpha. is a positive value, voltage signal Vz becomes smaller as ambient temperature T.sub.A is higher.
To reduce such influence of the ambient temperature, diode D whose forward voltage has a negative temperature coefficient may be connected in series with sensor element R.sub.Y, as shown in FIG. 6.
However, it is quite difficult to match the temperature coefficient of diode D with those of temperature sensor elements R.sub.X, R.sub.Y. Also, temperature compensation is not precisely achieved e.g. by variations in forward voltage of diode D and difference in temperature between diode D and temperature sensor elements R.sub.X, R.sub.Y which may occur if they are located separately.